Final answer:
The N-O bond lengths in NO3- are the same due to resonance stabilization, which averages the electron distribution across the molecule, resulting in resonance hybrid bonds of equal length and strength.
Step-by-step explanation:
The N-O bond lengths in the NO3⁻ molecule are the same because of resonance stabilization. The concept of resonance suggests that if more than one Lewis structure with the same arrangement of atoms can be written for a molecule or ion, the actual electron distribution is an average of those structures. Hence, the bonds in NO3⁻ do not actually alternate between single and double bonds; instead, all N-O bonds are of equal length and strength due to the averaging of their electron distribution across the molecule. This creates a resonance hybrid structure where the characteristics of the bonds are intermediate between a single and a double bond. Resonance forms are used to depict this averaging, joined by a double-headed arrow to indicate their equivalence.